Adaptation performance improvements for active control of sound or vibration

ABSTRACT

A noise or vibration control system improves the quality of adaptation estimates by filtering the input signals to the adaptation, selectively implementing a “dead-zone” during which adaptation does not occur and by selectively adding a dither signal to the control commands. The dead-zone is based on the magnitude of the changes in the control commands, which are responding to the changes in the sensor signals. The dead-zone can be applied to all actuators simultaneously, or can be applied to the adaptation of each actuator channel independently. To maintain identifiability, a “dither signal” is added to the control commands to “ping” the system to increase the amount of information available to the adaptive algorithm. The dither signal is preferably implemented on only one actuator channel at a time. Also, the dither amplitude for each channel is preferably set to be proportional to the current control amplitude. The quality of the adaptation estimates is also improved by filtering the input signals to the adaptation circuit, y k =Δz k , and v k =Δu k . Among other things, the filter matches the filtering applied by the harmonic estimator.

This application claims priority to U.S. Provisional Application Ser.No. 60/271,470, Filed Feb. 27, 2001.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to optimal control of a system such as an activenoise or vibration control system such as for a helicopter.

2. Background

An active control system consists of a number of sensors which measurethe ambient variables of interest (e.g. sound or vibration), a number ofactuators capable of generating an effect on these variables (e.g. byproducing sound or vibration), and a computer which processes theinformation received from the sensors and sends commands to theactuators so as to reduce the amplitude of the sensor signals. Thecontrol algorithm is the scheme by which the decisions are made as towhat commands to the actuators are appropriate.

For tonal control problems, the computation can be performed at anupdate rate lower than the sensor sampling rate as described incopending application entitled “Computationally Efficient Means forActive Control of Tonal Sound or Vibration”. This approach involvesdemodulating the sensor signals so that the desired information is nearDC (zero frequency), performing the control computation, andremodulating the control commands to obtain the desired output to theactuators. The control computations are therefore performed on the sineand cosine components at the frequency of interest for each sensorsignal. These can be represented as a complex variable where the realpart is equal to the cosine term, and the imaginary part is equal to thesine term.

The number of sensors is given by n_(s) and the number of actuators isn_(a). The complex harmonic estimator variables that are calculated fromthe measurements of noise or vibration level can be assembled into avector of length n_(s) denoted z_(k) at each sample time k. The controlcommands generated by the control algorithm can likewise be assembledinto a vector of length n_(a) denoted u_(k). The commands sent to theactuators are generated by multiplying the real and imaginary parts ofthis vector by the cosine and sine of the desired frequency.

In the narrow bandwidth required for control about each tone, thetransfer function between actuators and sensors is roughly constant, andthus, the system can be modeled as a single quasi-steady complextransfer function matrix, denoted T. This matrix of dimension n_(s) byn_(a) describes the relationship between a change in control command andthe resulting change in the harmonic estimate of the sensormeasurements, that is, Δz_(k)=TΔu_(k). For notational simplicity, definey_(k)=Δz_(k), and v_(k)=Δu_(k). The complex values of the elements of Tare determined by the physical characteristics of the system (includingactuator dynamics, the structure and/or acoustic cavity, andanti-aliasing and reconstruction filters) so that T_(ij) is the responseat the reference frequency of sensor i due to a unit command at thereference frequency on actuator j. Many algorithms may be used formaking control decisions based on this model.

The control law is derived to minimize a quadratic performance index

J=z ^(T) W _(z) z+u ^(T) W _(u) u+v ^(T) W _(δu) v

where W_(z), W_(u) and W_(δu) are diagonal weighting matrices on thesensor, control inputs, and rate of change of control inputsrespectively. A larger control weighting on an actuator will result in acontrol solution with smaller amplitude for that actuator.

Solving for the control which minimizes J yields:

u _(k+1) =u _(k) −Y _(k)(W _(u) u _(k) +T _(k) ^(T) W _(z) z _(k))

where

Y _(k)=(T _(k) ^(T) W _(z) T _(k) +W _(u) +W _(δu))⁻¹

The matrix Y determines the rate of convergence of different directionsin the control space, but does not affect the steady state solution. Inthe following equation, the step size multiplier β<1 provides controlover the convergence rate of the algorithm. A value of approximatelyβ=0.1 may be used, for example.

u _(k+1) =u _(k) −βY _(k)(W _(u) u _(k) +T _(k) ^(H) W _(z) z _(k))

The performance of this control algorithm is strongly dependent on theaccuracy of the estimate of the T matrix. When the values of the Tmatrix used in the controller do not accurately reflect the propertiesof the controlled system, controller performance can be greatlydegraded, to the point in some cases of instability. An initial estimatefor T can be obtained prior to starting the controller by applyingcommands to each actuator and looking at the response on each sensor.However, in many applications, the T matrix changes during operation.For example, in a helicopter, as the rotor rpm varies, the frequency ofinterest changes, and therefore the T matrix changes. For the gear-meshfrequencies, variations of 1 or 2% in the disturbance frequency canresult in shifts through several structural or acoustic modes, yieldingdrastic phase and magnitude changes in the T matrix, and instabilitywith any fixed-gain controller (i.e. if T_(k+1)=T_(k) for all k). Othersources of variation in T include fuel burn-off, passenger movement,altitude and temperature induced changes in the speed of sound, etc.

There are several possible methods for performing on-line identificationof the T matrix, including Kalman filtering, an LMS approach, andnormalized LMS. For an estimated T matrix, T^(e), an error vector can beformed as

E=y−T ^(e) v

The estimated T matrix is updated according to

T ^(e) _(k+1) =T ^(e) _(k) +EK ^(T)

The different estimation schemes differ in how the gain matrix K isselected. The Kalman filter gain K is based on the covariance of theerror between T and the estimate T^(e), given by the matrix P where

M=P _(k) +Q

K=Mv/(R+v ^(T)Mv)

P _(k+1) =M−Kv ^(T) M

and the matrix Q is a diagonal matrix with the same dimension as thenumber of actuators, and typically with all diagonal elements equal. Thescalar R can be set equal to one with no loss in generality providedthat the matrices Q and R are constant in time. The normalized LMSapproach is very similar, with the gain matrix K given by

K=Qv/(1+v ^(T)Qv)

The algorithm can be used with the Kalman filter approach, or using thenormalized LMS approach which is computationally simpler and may providesimilar or better performance. The current invention is described interms of this equation, however, the specific form of the adaptationalgorithm is not crucial to the invention.

Any of these adaptation schemes will obtain excellent estimation of theT matrix when there is little noise in the measurements. As noise levelsincrease, however, there are difficulties as the filter can notdistinguish between the effects of noise and the effects of actualchanges in T. As a result, the adaptation parameters will tend to drift.Decreasing adaptation gain will decrease the drift but not prevent it,and will degrade the adaptation performance.

The algorithm as described above is self-adaptive in the sense that theplant (i.e., system) model used in the control update calculation isactively updated during closed-loop operation based on changes in thesensor signals resulting from the application of the changes in theactuator commands determined by the control update calculation. However,during steady-state conditions, when changes in the control commands areresponding only to “noise” in the estimate of the disturbance beingcanceled, there is a loss of identifiability of the plant. This loss ofidentifiability is a result of coupling the control update calculationand the adaptation update calculation together. The adaptation processis estimating the system by observing how changes in actuator commandscause changes in the measured system response; however, due to thecontrol process, the change in control Δu is not independent from thechange in measurement Δz. This coupling results in an instability ordrift observed in steady state that can be severe if signal-to-noise ispoor.

In addition to causing drift behavior, as described above, noise alsodegrades the quality of the adaptation estimate through two relatedmechanisms. First, because the signal to noise ratio is reduced theadaptation estimate will include a random noise component. The secondeffect is more subtle. The adaptation is intended to estimate thetransfer function from actuators to sensors at the disturbancefrequency. It is reasonable to assume that the physical transferfunction does not vary substantially over the bandwidth of the control.Control transients are close to the disturbance frequency, and thereforethe transfer functions due to these input signals are close to thedesired transfer function. However, the adaptation will also respond tonoise on y_(k) and v_(k) that is at higher frequencies (in thedemodulated system, i.e. further away from the desired frequency).Changes in the physical system at these frequencies are unknown,however, the most significant change is due to the harmonic estimationfilter on y_(k), the effect of which is known. The estimation of theharmonic components of the sensor signals at the desired frequencyrequires low-pass filtering to avoid aliasing in downsampling theestimates. While there is no reduction in the amplitude of the sensorinformation y_(k) in the immediate vicinity of the desired frequency,y_(k) is attenuated at frequencies further form the desired frequency,while v_(k) is not. The algorithm described above will thereforeunder-predict the desired transfer function because it will average overfrequency, and include part of the reduction in amplitude of theharmonic estimator filter. There will be no bias in phase since thenoise for positive frequencies should be comparable to the noise fornegative frequencies, and the phase effects will therefore cancel.

SUMMARY OF THE INVENTION

The present invention improves the quality of the adaptation estimatesby filtering the input signals to the adaptation, selectivelyimplementing a “dead-zone” during which adaptation does not occur and byselectively adding a dither signal to the control commands. In thepresent invention, the dead-zone is based on the magnitude of thechanges in the control commands, which are responding to the changes inthe sensor signals. The dead-zone can be applied to all actuatorssimultaneously, or can be applied to the adaptation of each actuatorchannel independently. The appropriate threshold for the dead-zone canbe updated on-line.

To maintain identifiability, a “dither signal” is added to the controlcommands to “ping” the system to increase the amount of informationavailable to the adaptive algorithm. The dither signal is preferablyimplemented on only one actuator channel at a time. Further, it ispreferred that triangular dither is implemented such that the controlamplitude of the channel being dithered is ramped down and then rampedback up to its initial value in a predetermined number of steps. Also,the dither amplitude for each channel is preferably set to beproportional to the current control amplitude.

This invention will also improve the quality of the adaptation estimatesby filtering the input signals to the adaptation circuit, y_(k)=Δz_(k),and v_(k)=Δu_(k). Among other things, the filter matches the filteringapplied by the harmonic estimator.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows a block diagram of the noise or vibration control system ofthe present invention.

FIG. 2 shows a vehicle in which the present invention may be used.

DETAILED DESCRIPTION

Control systems consist of a number of sensors which measure ambientvibration (or sound), actuators capable of generating vibration at thesensor locations, and a computer which processes information receivedfrom the sensors and sends commands to the actuators which generate avibration field to cancel ambient vibration (generated, for example by adisturbing force at the helicopter rotor). The control algorithm is thescheme by which the decisions are made as to what the appropriatecommands to the actuators are.

FIG. 1 shows a block diagram 10 of an active control system. The systemcomprises a structure 102, the response of which is to be controlled,sensors 128, filter 112, control unit 107 and actuators (which could beforce generators) 104. A disturbance source 103 produces undesiredresponse of the structure 102. In a helicopter, for example, theundesired disturbances are typically due to vibratory aerodynamicloading of rotor blades, gear clash, or other source of vibrationalnoise. A plurality of sensors 128(a) . . . (n) (where n is any suitablenumber) measure the ambient variables of interest (e.g. sound orvibration). The sensors (generally 128) are typically microphones oraccelerometers, or virtually any suitable sensors. Sensors 128 generatean electrical signal that corresponds to sensed sound or vibration. Theelectrical signals are transmitted to filter 112 via an associatedinterconnector 144(a). . . (n) (generally 144). Interconnector 144 istypically wires or wireless transmission means, as known to thoseskilled in the art.

Filter 112 receives the sensed vibration signals from sensors 128 andperforms filtering on the signals, eliminating information that is notrelevant to vibration or sound control. The output from the filter 112is transmitted to control unit 107, which includes adaptation circuit108 and controller 106, via interconnector 142. In the presentinvention, a filter 109 is placed before adaptation circuit 108, as willbe described below. The controller 106 generates control signals thatcontrol force generators 104(a) . . . (n).

A plurality of actuators 104(a) . . . (n) (where n is any suitablenumber) are used to generate a force capable of affecting the sensedvariables (e.g. by producing sound or vibration). Force generators104(a) . . . (n) (generally 104) are typically speakers, shakers, orvirtually any suitable actuators. Actuators 104 receive commands fromthe controller 106 via interconnector 134 and output a force, as shownby lines 132(a) . . . (n) to compensate for the sensed vibration orsound produced by vibration or sound source 103.

The control unit 107 is typically a processing module, such as amicroprocessor. Control unit 107 stores control algorithms in memory105, or other suitable memory location. Memory 105 is, for example, RAM,ROM, DVD, CD, a hard drive, or other electronic, optical, magnetic, orany other computer readable medium onto which is stored the controlalgorithms described herein. The control algorithms are the scheme bywhich the decisions are made as to what commands to the actuators 104are appropriate, including those conceptually performed by thecontroller 107 and adaptation circuit 108. Generally, the mathematicaloperations described in the Background, as modified as described below,are stored in memory 105 and performed by the control unit 107. One ofordinary skill in the art would be able to suitably program the controlunit 107 to perform the algorithms described herein. The output of theadaptation circuit 108 may be filtered before being sent to thecontroller 107.

The present invention improves the quality of the adaptation estimatesby adaptation circuit 108 by filtering the input signals to theadaptation circuit, selectively implementing a “dead-zone” during whichadaptation does not occur and by selectively adding a dither signal tothe control commands.

The filtering, dead zone and dither can be used independently; however,dead zone is beneficial to overcome the drift behavior and dither isbeneficial to maintain good performance while using dead zone.

Dead zone

One way to avoid the aforementioned loss of identifiability duringsteady-state conditions is to actively interrogate the system todetermine if the operating conditions are fairly steady and if so turnadaptation off, and only turn it back on again when the system is nolonger in a steady-state condition. This approach is usually referred toas establishing a “dead-zone” in which adaptation does not occur.Usually, this dead-zone is established based on examining the magnitudeof changes in the sensor signals from one iteration to the next, and ifthey are smaller than some predefined level, turning adaptation off, andif above that level, turning adaptation on. In the present invention,the dead-zone is based instead on the magnitude of the changes in thecontrol commands, which are responding to the changes in the sensorsignals. The variable Δu provides a good estimate of whether there areany significant changes that require adaptation to be turned on. Anychange in the system T matrix will result in changes in Δu. The use of||Δu|| as the dead-zone switch is motivated by the fact that there issome minimum value of ||Δu|| required for each channel to achieve a goodsignal-to-noise ratio.

The dead-zone can be applied to all actuators simultaneously, or can beapplied to the adaptation of each actuator channel independently (i.e.to each column of the T matrix independently). With the former, thenevery element of the diagonal matrix Q is equal and set according toq=q₀ if ||Δu||>Δ_(z) and q=0 otherwise, where Δ_(z) is the dead-zonethreshold. If the dead-zone is instead applied to each channel, theneach element of the diagonal matrix Q is either zero if thecorresponding |Δu_(i)|<Δ_(z), or set equal to q₀ otherwise. SettingQ(i)=0 turns adaptation off for channel i, and setting it to somepositive number greater than zero turns adaptation on. Performing thedead-zone comparison on an actuator channel-by-channel basis ispreferable.

Rather than switching adaptation only between on and off, the adaptationgain can be any function of |Δu| that is small for small |Δu|, someconstant for large |Δu|, and goes through some transition in between.For example, setting q=min (q₀, q_(v)|Δu|^(N)) has been tested, where Nis an integer typically between 2 and 6. Again, this can be setindependently for each actuator channel, or the absolute value can bereplaced by a norm of the overall vector and the adaptation gain setequal for all channels.

A further refinement of this approach is to actively adjust orrecalculate the dead-zone threshold for each actuator channel based onthe current noise floor and actuator 104 effectiveness. The dead-zonethreshold for each channel is obtained by slowly filtering the dead-zoneparameter |Δu_(i)| and multiplying the result by a scale factortypically between 2 and 3. The filter time constant can be 100 timeslarger than the adaptation time constant.

Dither

The second aspect of this invention is to ensure that the adaptationalgorithm has sufficient information to accurately identify the system.To maintain identifiability, a “dither signal” is added to the controlcommands to, in essence, “ping” the system to increase the amount ofinformation available to the adaptive algorithm. Although it is known toadd a dither signal to this type of system, there are several uniqueaspects of the dither signal implementation in the present invention.

First, the dither signal is implemented on only one actuator channel ata time. Because only a single channel is dithered, then a largeramplitude can be used without degrading overall performancesignificantly, and hence a larger signal-to-noise ratio is obtained. Allof the information coherent with the injected dither signal can beassociated with the dithered actuator 104 channel.

The channel being dithered is removed from the control updatecalculation with a high control weighting, while being the only channelincluded in the adaptation update calculation. This modificationdecouples the control and adaptation behavior so that the adaptationrecovers its ideal open-loop behavior, and avoids any possibility ofdrift. Furthermore, any sensor information resulting from the ditherwill not corrupt the system transfer function estimates for any of theother actuators. The system looks at the response of the sensors 128taking into account the fact that the actuators 104, other than thedithered actuator, have compensated for the dither signal added to thedithered actuator.

Triangular dither is implemented such that the control amplitude of thechannel being dithered is ramped down and then ramped back up to itsinitial value in a predetermined number of steps. The motivation forramping the control amplitude down first and then back up to itsoriginal value is that in the case where the dithered channel is upagainst the saturation limit (maximum allowable actuator command) beforethe application of dither, then the dither will bring the actuator 104down off this limit. Alternatively, if the dither were implemented firstas a ramp up in amplitude followed by a ramp down, then in the case ofsaturation, control limiting (i.e., signal clipping) would prevent thedither from being implemented since the actuator 104 would be up againstthe saturation limit throughout the entire dither cycle. Other types ofdither signal are possible; however, the ramp maximizes the variable Δuwhich is used by the adaptation algorithm.

The dither amplitude for each channel is set to be proportional to thecurrent control amplitude. This is desirable because not all actuatorshave equal authority. An actuator 104 with higher authority requireslower control amplitude to achieve the same output or signal to noiseratio. Using this improvement will therefore result in a lower ditheramplitude for such an actuator, which, due to the higher authority, willresult in similar signal-to-noise for all actuators. Without thismodification, a fixed dither amplitude for every actuator 104 wouldrequire that a large amplitude be used for sufficient signal-to-noise onthe lower authority actuators, which would then yield significantperformance degradation of the control system while dithering the higherauthority actuators. An additional benefit of a proportional dithersignal is to provide more information in highly uncertain directions. Ifsome information in the estimate of the T matrix has more error thanother information, this will tend to result in larger than necessaryamplitudes on the control signals corresponding to the bad information.As a result, the dither amplitude will increase for these controlsignals, providing more information to correct the poorer T matrixestimates. If the estimate of the T matrix is known to be poor, forexample when the active control system is first activated, then a morerapid adaptation convergence can be obtained by temporarily increasingthe dither amplitude and/or the adaptation gain.

This invention will also improve the quality of the adaptation estimatesby filtering the input signals to the adaptation circuit 108,y_(k)=Δz_(k), and v_(k)=Δu_(k) with filter 109. The presence ofbackground noise not only results in parameter drift, but results inboth a bias and a random error in the elements of the T matrix estimate.Improving the quality of the estimate improves the achievableperformance of the control algorithm. Alternately, the same qualityestimate can be achieved, and the invention can be used to allow loweramplitude dither signals to obtain similar adaptation performance, andlower degradation in overall performance due to the dither.

Introducing a matching first-order low-pass filter on the signal v_(k)corrects for the bias effect caused by the adaptation responding tonoise which has been filtered through the harmonic estimator. Thismatching filter must have the same corner frequency as the harmonicestimator filter. The result is improved signal to noise due to loweremphasis on high frequency noise, and eliminating bias in the estimate.

The adaptation algorithm described in the background uses the differencein z and u between samples, Δz=z_(k)−z_(k−1) and Δu=u_(k)−u_(k−1), inorder to avoid variations in the ambient near zero frequency fromdistorting the transfer function estimate. This differencing amplifieshigher frequency content in u and z. The combination of this with theharmonic estimator filter on z and its matching filter on u results inall information at frequencies above the harmonic estimator cornerfrequency being treated with equal importance, and information belowthis frequency being treated with lower importance. Since theinformation at higher frequencies is predominantly noise rather thanuseful information, including additional low-pass filtering on both thesignals v_(k) and y_(k) will improve signal to noise ratio, and improvethe quality of the T-matrix estimate (or conversely, allow the samequality of estimate with a lower amplitude dither signal, and henceimprove overall algorithm noise reduction performance.) This low-passfiltering can be implemented either as a separate step, or by changingthe difference definition of v_(k) and y_(k) to a high-pass filter. Theresult of the combination of filters is to put the most emphasis on theinformation at the frequencies around the filter corner frequencies, andless emphasis on the information at lower and higher frequencies.

A further modification of the above filtering could improve adaptationperformance by using a separate set of filters on the informationgenerated by control transients, and the information generated by thedither signal. The filter characteristics can then be optimized for theknown frequency domain characteristics of each of the two types ofcontrol inputs u_(k), in order to maximize the signal to noise ratio foreach.

A final modification to the above concept could be useful in systemswith small numbers of actuators. The dither algorithm contained in thisinvention uses time separation to distinguish between the information onone actuator 104 and the information on another, and this is appropriateif there are many actuators. If there are very few actuators, thenfrequency separation could be used instead. That is, one could put acontinuous, small amplitude dither signal on each actuator command, witha different frequency for each actuator. Second-order resonant filterson both v_(k) and y_(k) could then be used to extract the distinctinformation corresponding to each frequency.

FIG. 2 shows a perspective view 20 of a vehicle 118 in which the presentinvention can be used. Vehicle 118, which is typically a helicopter, hasrotor blades 119(a) . . . (d). Gearbox housing 110 is mounted at anupper portion of vehicle 118. Gearbox mounting feet 140(a) . . . (c)(generally 140) provide a mechanism for affixing gearbox housing 110 tovehicle airframe 142. Sensors 128(a) through (d) (generally 128) areused to sense acoustic vibration produced by the vehicle, which can befrom the rotorblades 119 or the gearbox housing 110. Although only foursensors are shown, there are typically any suitable number of sensorsnecessary to provide sufficient feedback to the controller (not shown).The sensors 128 may be mounted in the vehicle cabin, on the gearboxmounting feet 140, or to the airframe 142, or to another location on thevehicle 118 that enables vehicle vibrations or acoustic noise to besensed. Sensors 128 are typically microphones, accelerometers or othersensing devices that are capable of sensing vibration produced by gearclash from the gearbox 110 and generating a signal as a function of thesensed vibration. These sensors generate electrical signals (voltages)that are proportional to the local noise or vibration.

In accordance with the provisions of the patent statutes andjurisprudence, exemplary configurations described above are consideredto represent a preferred embodiment of the invention. However, it shouldbe noted that the invention can be practiced otherwise than asspecifically illustrated and described without departing from its spiritor scope. Alphanumeric identifiers for steps in the method claims arefor ease of reference by dependent claims, and do not indicate arequired sequence, unless otherwise indicated.

What is claimed is:
 1. A method for reducing sensed physical variablesincluding the steps of: a) generating a plurality of control commands asa function of the sensed physical variables based upon an estimate of arelationship between the sensed physical variables and the controlcommands; b) updating the estimate of the relationship based upon aresponse by the sensed physical variables; and c) varying a size of theupdate to the estimate in said step b) based upon a magnitude of changeover time by at least one of the plurality of control commands, whereinthe estimate of the change in response y=Δz due to a chance in controlcommand v=Δu at a specific time t_(k) is denoted T_(k), where T_(k) isupdated according to the equations T _(k+1) =T _(k) +EK ^(T) E=y−T _(k)v K=Qv/(1+v ^(T)Qv), the matrix Q is a diagonal matrix with elementsq_(i), and the variables q_(i) determine the adaptation gaincorresponding to the i^(th) control command.
 2. The method of claim 1further including the step of selecting between updating or leavingunchanged the estimate of the relationship based upon a magnitude ofchange by the plurality of control commands.
 3. The method of claim 1further including the step of: d) selecting between updating or leavingunchanged the estimate corresponding to a first control command of theplurality of control commands based upon the magnitude of the change inthe first control command.
 4. The method of claim 3 further includingthe steps of comparing the magnitude of the change to a threshold andvarying the threshold based upon an estimate of a signal to noise ratio.5. The method of claim 1 wherein: a) each variable q_(i) at each timestep is set equal to zero or to some nominal value depending on whether|v_(i)|>δ_(i) where |v_(i)| is a magnitude of change in the i^(th)control command and the variables δ_(i) are the deadzone threshold forchannel i.
 6. The method of claim 1 wherein: each variable q_(i) at eachtime step us set according to the equation q_(i)=max (q_(o),q_(v)|v_(i)|^(N)) where q_(o) and q_(v) are parameters chosen for aparticular application, |v_(i)| is a magnitude of change in the i^(th)control command and N is a positive integer.
 7. The method of claim 1wherein the estimate of the relationship is given by Δz=TΔu, where Δz isa change in the sensed physical variables and Δu is a change in thecontrol commands.
 8. A method for reducing sensed physical variablesincluding the steps of: a) generating a plurality of control commands asa function of the sensed physical variables based upon an estimate of arelationship between the sensed physical variables and the controlcommands; b) updating the estimate of the relationship based upon aresponse by the sensed physical variables; c) where the control commandsare filtered to match a filter that has been applied to the sensedphysical variables to improve the quality of the estimates prior to saidstep b); and wherein a change in the sensed physical variables Δz isrelated to a change in the control commands Δu by Δz=T(Δu), the estimateof a sensed physical variable response T is based on Δu and Δz, saidmethod further including the step of filtering Δu to match a knownfilter on Δz.
 9. The method of claim 8 further including the step oflow-pass filtering both Δu and Δz to reduce an impact of high-frequencynoise on the estimate of T.
 10. A system for controlling a plurality ofsensed physical variable comprising: a plurality of sensors formeasuring the physical variables; a control unit generating an estimateof a relationship between the sensed physical variables and a pluralityof control commands, and generating the plurality of control commandsover time based upon the sensed physical variables and based upon therelationship; and a plurality of force generators activated based uponsaid plurality of command signals; wherein the control unit sequentiallyadds a signal to each of the plurality of control commands, measures theresponse to the signal and updates the estimate of the relationshipbased upon the response, wherein the signal added by the control unit isa dither signal that initially decreases in order to avoid saturationfor that control command.
 11. The system of claim 10 wherein the signaladded to each of the plurality of control commands by the control unitdiffers for each control command.
 12. The system of claim 11 wherein thesignal added to a given control command includes a triangular signal.13. The system of claim 10 wherein the control unit holds constant thecontrol command to which the signal is added and updates the controlcommands other than the one to which the signal is added according tothe relationship.
 14. The system of claim 13 wherein the control unitupdates the relationship only for the control command to which thesignal is added.
 15. The system of claim 10 wherein the control unitdetermines a magnitude of the signal based upon a current magnitude ofthe control command to which the signal is added.
 16. The system ofclaim 10 wherein the control unit varies a frequency of the signal to beadded to each of the plurality of control commands and extracts theinformation corresponding to each said control command.
 17. A system forcontrolling a plurality of sensed physical variable comprising: aplurality of sensors for measuring the physical variables; a controlunit generating an estimate of a relationship between the sensedphysical variables and a plurality of control commands, and generatingthe plurality of control commands over time based upon the sensedphysical variables, and based upon the relationship; and a plurality offorce generators activated based upon said plurality of command signals;wherein the control unit varies a size of the update to the estimate ofthe relationship based upon a magnitude of change over time by at leastone of the plurality of control command and wherein the control unitselects between updating or leaving unchanged the estimate of therelationship based upon a magnitude of change by the plurality ofcontrol commands.
 18. The system of claim 17 wherein the control unitcompares the magnitude of the change to a threshold and varies thethreshold based upon an estimate of a signal to noise ratio.
 19. Thesystem of claim 18 wherein the estimate of the change in response y=Δzdue to a change in control command v=Δu at a specific time t_(k) isdenoted T_(k), where T_(k) is updated according to the equations T_(k+1) =T _(k) +EK ^(T) E=y−T _(k) v K=Qv/(1+v ^(T)Qv), the matrix Q isa diagonal matrix with elements q_(i), and the variables q_(i) determinethe adaptation gain corresponding to the i^(th) control command.
 20. Thesystem of claim 19 wherein the control unit sets each variable q_(i) tozero or some nominal value at each time step depending on whether|v_(i)|>δ_(i) where |v_(i)| is a magnitude of change in the i^(th)control command and the variables δ_(i) are a deadzone threshold forchannel i.
 21. A method for reducing sensed physical variables includingthe steps of: a) generating a plurality of control commands as afunction of the sensed physical variables based upon an estimate of arelationship between the sensed physical variables and the controlcommands; b) updating the estimate of the relationship based upon aresponse by the sensed physical variables; and c) varying a size of theupdate to the estimate in said step b) based upon a magnitude of changeover time by at least one of the plurality of control commands, whereinthe estimate of the relationship is given by Δz=TΔu, where Δz is achange in the sensed physical variables and Δu is a change in thecontrol commands, and wherein the size of the update is varied in saidstep c) based upon a comparison of ||Δu|| to a threshold.
 22. The methodof claim 21 further including the step of selecting between updating orleaving unchanged the estimate of the relationship based upon thecomparison of ||Δu|| to a threshold.